Gap probabilities and applications to geometry and random topology

Non-equilibrium Dynamics and Random Matrices
Topic:Gap probabilities and applications to geometry and random topology
Speaker:Antonio Lerario
Affiliation:Purdue University
Date:Wednesday, October 30
Time/Room:4:30pm - 5:30pm/S-101
Video Link:https://video.ias.edu/nedrm/2013/1030-AntonioLerario

What is the volume of the set of singular symmetric matrices of norm one? What is the probability that a random plane misses this set? What is the expected "topology" of the intersection of random quadric hypersurfaces? In this talk I will combine classical techniques form algebraic topology ("spectral sequences") with ideas from Random Matrix Theory and show how these problems can be solved using a local analysis of the "gap probability" at zero (the probability that a random matrix has a gap in its spectrum close to zero). (This is a joint work with E. Lundberg.)